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11 T Nb3Sn magnet thermal model (1/5)

5/25/2012 7th Collimation Upgrade Specification meeting

Equations: energy equations considered for solid and superfluid helium

One heat exchanger at 1.9 K 25 % wetted by liquid HeII

Homogenization of the cable at the first order taking account of the copper, the Nb3Sn and the resin: effective thermal conductivity kcable(T)

Cable insulation (G-10 – 100 µm thick) modeled by a thermal resistance

Between inner/outer coil: 3 layers of G-10 168 µm thick modeled by one layer 504 µm thick

Between the coils and collars: 5 layers of kapton 125 µm thick modeled by one layer 625 µm thick

Titanium pole piece is taken 4 % open

Collars and yoke laminations are taken 2 % open

Annular space 1 – 1.5 mm

25/25/2012 7th Collimation Upgrade Specification meeting

11 T Nb3Sn magnet thermal model (2/5)

Input: assumed heat load distribution corresponding to 1.5 W/m

35/25/2012 7th Collimation Upgrade Specification meeting

11 T Nb3Sn magnet thermal model (3/5)

45/25/2012 7th Collimation Upgrade Specification meeting

11 T Nb3Sn thermal model (4/5)

Maximum Temperature 2.39 K at midplane

55/25/2012 7th Collimation Upgrade Specification meeting

11 T Nb3Sn thermal model (5/5)

Next to be done:

simulations with the real heat load

more precise homogenization of the cable

quench analysis to determine:

- holes in titanium piece needed- maximum pressure reached

transient analysis

Conclusions:

T-map-results invariant of annular space in range 1 – 1.5 mmT-map-results invariant pole piece opening in range 1 – 4 %

With respect to LHC main dipole construction we assume that 1.5 mm annular space and 4 % pole piece opening are safe to cope with quench overpressure.Could be minimized, but would need verification (to be done)